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Handbook of Mathematics Index © Copyright 2015. Index A-basis, 316 Adjoint functor, 302 A-module, 316 Adjoint functors, 595 Ab-category, 585 Adjoint functors (adjunction), 595 Ab-enriched (symmetric) monoidal category, 586 Adjoint map, 243 Abel lemma, 121, 453 Adjoint of a linear map, 243 Abel theorem, 129 Adjoint operator, 243, 375 Abel-Poisson, 487 Adjoint pair (of functors), 311 Abelian category, 584, 591 Adjointness, 589 Abelian group, 42, 43, 82, 84, 88, 89, 103, 474, 475, 516, 517, 521, 584, 590, Adjunction, 595 599 Adjunction isomorphism, 596 Abelian integral, 437 Adjunction of indeterminates, 120 Abelian semigroup, 43, 516 Admissible open set, 306 Abelian variety, 513 Admissible parameter, 393 Abelianization, 315 Admissible parameterization, 393 Abraham-Shaw, 748 Affine algebraic set, 513 Absolute complement, 8, 12 Affine bijection, 169 Absolute consistency, 5 Affine combination, 278 Absolute extrema, 45 Affine connection, 417, 418 Absolute frequency, 620 Affine coordinates system, 190 Absolute geometry, 149, 151, 152 Affine endomorphism, 191 Absolute gometry Affine form, 191 models 1,2,3,4, 151 Affine geometry, 155 Absolute homology groups , 291 Affine group, 168 Absolute Hurewicz theorem, 315 Affine independent, 278 Absolute maximum, 670 Affine independent set, 278 Absolute valuation, 79 Affine isometry, 187 Absolute value, 145 anti-displacement, 187 in the field of rationals, 145 displacement, 187 non-Archimedean, 145 Affine map, 168, 169 Absolute value of a rational number, 62 A ffi ne m ap in R3, 186 Absolutely convergent series, 324 Affine morphism, 564 Absolutely flat ring, 526 Affine n-chain, 293 Absorbing, 33 A ffi ne n-space, 270 Absorbing element, 12, 33 Affine neighborhood, 569 Absorbing on the left, 33 Affine orthogonal symmetry, 168 Absorbing on the right, 33 Affine plane, 155 Absorption, 8, 9 Affine plane of incidence, 155 Absorption laws, 12 Affine scheme, 270, 513, 563, 566 Abstract algebra, 263, 509 Affine set, 277 Abstract algebraic variety, 513 Affine set (convex set), 277 Abstract category, 38, 598 Affine space, 189, 277, 531 Abstract Riemann surface, 432 affine subspace, 190 Abstract simplicial complex, 295, 534 canonical structure, 190 Abstract space, 370 vectorial structure, 190 Abstract variety, 513 Affine space (algebraic geometry), 531 Acceptance region, 617 Affine space (analytic geometry), 531 Accumulation point, 26, 195, 198 Action-angle variable, 695 Affine subspace, 190 Acwise connectedness, 546 Affine subspace intersection, 190 Acyclic carrier, 304 Affine symmetry, 168 Acyclic complex, 290 Affine transformation, 169 Acyclic cover, 296 Affine variety, 264, 513, 531 Acyclic cover of a simplicial complex, 296 Affine Y-scheme, 564, 570 Acyclic free chain complex, 303 Affines map, 190 Acyclic free chain complex theorem, 303 Affinity, 168, 169 Acyclic graph, 260 A ffi x, 69, 71 Acyclic model, 303 Afraimovich-Shilnikov theorem, 739 Acyclic models, 303 Aggregate demand function, 677 Acyclic object, 556, 557 Agument predicate, 3 Acyclic resolution, 559 AIC and SC criteria, 647 Acyclic sheaf, 559 AIC criteria, 647 Acyclic space, 287 AIC criterion, 632 Aczel’s constructive Zermelo-Fraenkel (CZF), 16 A IC (p), 647 Addition and multiplication in N, 52 Aitken estimator, 633 A ddition in N, 52 Akaike criterion (AIC), 640 A ddition in Q, 61 Akaike function, 632 A ddition in Z, 58 Akaike information criterion, 632 Additive abelian group, 82 Akaike-Schwarz, 629 Additive associativity, 43, 516 Akaike-Schwarz criteria, 647 Additive category, 585 Alembert theorem, 224 Additive commutativity, 43, 516 A leph, 33 Additive functor, 303, 597 Aleph-0, 33, 35, 37 Additive group, 103 Aleph-1, 33, 35, 48 Additive group of integers modulo n, 87 Alexander-Veblen corollary, 296 Additive identity, 42, 43, 516 Alexander-Whitney theorem, 319 Additive inverse, 42, 43, 516 Alexandroff compactification, 210 Additive notation, 32, 39 Alexandroff extension, 210 additively and multiplicatively stable, 40 Alexandroff theorem, 225 Additively stable, 40 Algebra, xvii, 81, 133, 264 Additivity axiom, 553 associative, 133 Adequate, 297 commutative, 133 Adequate subcomplex, 297 of Banach, 442 Adherent point, 195, 198, 219, 674 σ-algebra (Σ-algebra, Ω-algebra), 511 Adherent point of a filter, 223 Algebra of polynomials, 107 Adic topology, 533, 569 Algebra of sets, 8 A djective Algebra of the disk, 460 autological, 13 Algebraic basis, 244 heterological, 13 Algebraic category, 593 Adjoint, 607 Algebraic closure, 69, 77, 124, 531 Adjoint endomorphism, 137 Algebraic closure of a field, 69, 78 7 7 9 Index Algebraic closure of C, 77 Antidual, 405 Algebraic complex numbers over Q, 117 Antidual basis, 405 Algebraic curve, 150, 336 Antihomomorphism, 562 Algebraic dimension, 212 Antilinear map, 241 Algebraic dual, 238 Antinomy, 13 Algebraic element, 530 semantic or syntactic, 13 Algebraic elements of a field, 122 Antipodal map, 294 Algebraic extension, 123 Antipode, 271, 294 Algebraic extension of a field, 69, 531 Antisymmetric function, 138 Algebraic function, 335, 436 Antisymmetric map, 138 Algebraic fundamental group, 568 Antisymmetric multilinear form, 138 Algebraic geometry, 509 Antisymmetrization, 138 Algebraic K-theory, 269, 562 Antisymmetrization operator, 138 Algebraic number, 78, 117 Antisymmetry, 7 Algebraic number field, 78 Aperiodic solution, 722 Algebraic operation, 8, 510 Apollonius circle, 167 Algebraic operations in sets, 8 Apollonius definition of a circle, 168 Algebraic point, 437 Applied mathematics, xviii Algebraic problem, 129 Approximation, 331 Algebraic ramification, 433 Approximation by convolution, 491 Algebraic relation, 335, 336 Approximation by interpolation polynomial, 340 Algebraic representation of a complex number, 70 Approximation by polynomials Algebraic set, 513 on a compact of Cn, 236 Algebraic signature, 511 on a compact of Rn, 236 Algebraic space, 513 Approximation by trigonometric polynomials, 236 Algebraic structure, 38, 81, 512, 514, 582 Approximation methods, 354 of integers, 64 Approximation of vector functions, 236 of rationals, 65 Approximation theory, 338 of real numbers, 66 AR (autoregressive), 644 Algebraic structure of R, 321 AR model, 644 Algebraic surface, 150 AR(p), 634, 644 Algebraic system, 265, 280, 510 Arc, 196, 204 Algebraic topology, xvii, 247, 270, 509 Arc length, 358 Algebraic variety, 264, 513 Arc length of curve, 358 Algebraically closed, 77 Arc length parameterization, 499 Algebraically closed field, 78, 113, 531, 569 Arc of a curve, 392, 393 Algebras for a monad, 593 ARCH (AR conditional heteroscedasticity), 637 Algebrization, 129 ARCH model, 637 Almost everywhere convergence, 488 ARCH test, 637 Alternating algebra, 137 ARCH(q), 652 Alternating bilinear form, 449 Archimedean property, 52, 67 Alternating form, 138 Archimedean totally ordered commutative field, 66 Alternating group, 87, 138 Archimedean totally well ordered field, 78 Alternating map, 138 Archimedean valued field, 146 Alternating series, 324 Arcwise-connected, 545, 546 Alternative hypothesis H 1, 617 Arcwise-connected component, 204 Altitude, 166 Arcwise-connected set, 196, 204 Ambient manifold, 544 Arcwise-connected space, 204, 226, 545 Amenable group, 18 Area function, 168 Amnestic functor, 595 Area measure on a regular patch, 400 Ampère law, 364 Area of elliptic triangle, 179 Amplitude of cycle, 734 Area problem, 328 Amplitude spectrum, 662 Areolar function, 365 Analysis, xviii, 321 Areolar measure, 365 Analysis of autocorrelation function, 643 ARFIMA (AR fractionally integrated MA), 651 Analysis of residuals, 646 ARFIMA process, 651, 652 Analysis of shocks, 647 ARFIMA(p,d,q), 651, 652 Analysis of variance, 617 Argand-Cauchy plane, 71 Analysis of variance (ANOVA), 627 Argand-Gauss plane, 71 Analysis situs, xvii Argument, 2, 74, 455, 499 Analytic, 548 Argument of a complex number, 74 Analytic at, 548 Argument principle, 476 Analytic continuation, 421, 427, 441, 457 ariety (universal algebra), 513 Analytic continuations along different paths, 427 ARIMA (AR integrated MA), 644 Analytic function, 333, 415, 426, 433, 548 ARIMA model, 644 Analytic function at a point, 548 ARIMA process, 645 Analytic function on interior of domain, 548 Arithmetic, 51 Analytic functions, 421 Arithmetic function, 141 Analytic geometry, xvii, 130, 149, 181 Euclidean, 142 real or complex, 150 Arity, 510, 511 Analytic manifold, 540 ARMA (autoregressive moving average), 645 Analytic representation, 172 ARMA model, 645 Analytic set, 560 ARMA(p,q), 645 Analytic space, 560 A R M A X , 646 Analytic subspace, 560 Arnold, 687, 695 Analytic variety, 513 Arnold tongue, 742 Andronov-Hopf bifurcation, 735, 748 Arnold tongues, 740 Andronov-Hopf theorem, 735 Arrangement, 613 Andronov-Pontryagin theorem, 724 Arrangements with repetitions, 614 Andronov-Witt theorem, 719 Arrangements without repetition, 614 Angle, 160, 163 A rrow , 576 acute, 160 Arrowsmith-Place, 708, 712 obtuse, 160 Articulation vertex, 262 of opening, 184 Artin braid group, 539 refl ex, 160 Artinian ring, 525 right, 160 Artinian set, 35 straight, 160 Ascending chain condition (ACC), 523 Angle measure, 191 Ascoli theorem, 236, 442 Angle measure on a regular patch, 400 Associate, 309 Angle measurement, 161 Associative law, 41 Angle trisection, 75, 130 Associative magma, 41, 515 Angle-preserving transformation, 438 Associativity, 8, 9 Annihilating element, 12 Associativity isomorphism, 587 Annulus, 195, 428, 447, 450, 464 Associator, 586 A nosov, 705 Astroid, 336 Anosov automorphism, 703 Asymptote, 334 Anosov diffeomorphism, 705, 732 Asymptotic behavior of Fourier coefficients, 655 ANOVA equation, 627 Asymptotic line, 403 ANOVA table, 617 Asymptotic point, 381 for simple regression
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